1969.Conics Intersecting Cubic Curves At a Fixed Point

 Let P be a triangle center on K001-Neuberg Cubic of ABC.

Any line through P intersect the  K001-Neuberg Cubic at P1 and P2.

*As P1, P2 varies on K001-Neuberg Cubic, the conic {A,B,C,P1,P2} intersect the K001-Neuberg Cubic at a fixed point.

**If P=X(1)-Incenter of ABC, fixed point is X(7164).

    If P=X(3)-Circumcenter of ABC, fixed point is X(1138).

    If P=X(4)-Orthocenter of ABC, fixed point is X(8431).

    If P=X(13)-1st Fermat-Toricelli point of ABC, fixed point is X(8445).

    If P=X(399) of ABC, fixed point is X(4).  

1962. A Type of Bicevian Conic

1948. Gergonne-Nagel Conic

1947. A Conic Problem

1946. A-Mixtilinear Hyperbola

1945. Conics Related To Euler Line

1934.A Property Of Jerabek Hyperbola

1930. Remarks On A General Conic

1911. Conic of Inverse points

1899. A Locus For K001-Neuberg Cubic (Part 5)

1877. A Property Of Rectangular Circumhyperbola

1874. A Family Of Conics Centered at X(5)-NPC Center (Part 2)

1873. A Family Of Conics Centered at X(5)-NPC center

 Lat ABC be an acute angled triangle and P be a point.

A1B1C1-cevian triangle of P and A2B2C2-circumcevian triangle of P.
Oba=Circumcenter of (BA1A2),  Oca=Circumcenter of (CA1A2).
Circle through the points A2,Oba, Oca intersects the BC at A3, A4.
Define B3,B4,C3,C4 cyclically.

*A3, A4, B3, B4, C3, C4 lie on same conic. For all P, center of conic is X(5)-NPC center.
Are there any remarkable properties of perspectors of these family of conics?

1869. A Locus For K001-Neuberg Cubic (Part 4)

1865. A Locus For K001-Neuberg Cubic (Part 3)

1861. A Locus For K001-Neuberg Cubic (Part 2)

1860. A Locus For K001-Neuberg Cubic of ABC

1831. ConConic Triangles

 Let P be a point and A1B1C1 cevian triangle of P.

ta= tangent to circumcircle of A1B1C1 at A1. Define tb, tc cyclically.
Let A2B2C2 triangle bounded by lines ta, tb, tc.

*A,B,C, A2,B2,C2 lie on same conic.
** For P=X(2), Center of the conic is X(15449)-CENTER OF THE X(2)-ALTINTAS HYPERBOLA.
*** Which is the center of the conic for some triangle centers?

1817.

1797. Conic Problem